In the interview with CNN, Landry also suggested that such protections for people with existing medical problems might not be necessary if former President Barack Obama's signature health care law was overturned because a more competitive health insurance market would "eliminate the pre-existing condition issue."

"I believe the Republican Party has always taken the position that we would like to prohibit insurance companies from penalizing citizens for pre-existing conditions," Landry said. "We believe that by engaging the marketplace -- by ripping down the barriers, by adding more competition into the marketplace -- you lower those particular premiums."

Louisiana House Speaker Taylor Barras, R-New Iberia, said legislative leaders would work to preserve the mandate for health care coverage for people with pre-existing conditions in Louisiana, should Landry's lawsuit get the current federal mandate thrown out.

"Should the litigation in Texas be successful, I would encourage the Governor to engage the Legislature immediately to review options for Louisiana," Barras said in a written statement. Barras did not say how the Legislature would go about keeping the requirement to cover pre-existing conditions in place.

Landry is one of 20 Republican attorneys general and governors who have brought a lawsuit asking a Texas federal court judge to overturn the Affordable Care Act. Texas Attorney General Ken Paxton is leading the effort.

"I'm not the legislature, I'm the Attorney General making sure that we abide by the rule of law," says Louisiana AG Jeff Landry when pressed on whether there's a plan for people with pre-existing conditions to keep healthcare if a GOP lawsuit to bring down Obamacare is successful pic.twitter.com/t8OiVjwQuN

If the lawsuit is successful, protections for people with pre-existing health conditions that ensure they have access to health insurance and limits on how much older people can be charged for health care plans could get struck down. Paxton and Landry are asking for all Obamacare provisions to be declared null and void.

Even if the court doesn't agree to throw out the law, Paxton's office argued last week that it should still consider getting rid of the mandate that health insurance companies have to cover pre-existing conditions in the 20 states bringing the lawsuit.

According to Paxton, Congress' decision to get rid of the financial penalty for people who don't sign up for health insurance in 2019 makes it difficult to require that health insurers also cover people with ongoing medical problems. His office has argued that one mandate can't exist without the other.

In Louisiana, 849,000 non-elderly adults -- about 30 percent of the state's non-elderly adult population -- have a pre-existing medical condition and could have difficulty obtaining health insurance if the Affordable Care Act was repealed or altered, according to the Kaiser Family Foundation. People with pre-existing conditions often struggled to find health insurance before the law went into effect, particularly if they switched jobs or were self-employed.

If the lawsuit got the pre-existing condition coverage mandate thrown out in Louisiana, Landry said it would be up to state lawmakers to determine whether a statewide mandate would go into place to replace it. "I think that would be a debate we would have the Capitol and the Legislature would make that particular determination," Landry told CNN.

"I'm not the Legislature. I'm the attorney general making sure we abide by the rule of law," Landry said.

Barras agreed that finding a solution to keeping health care coverage for people with ongoing medical problems -- if the current one was thrown out by Landry's lawsuit -- would be up to the Legislature.

"We stand ready to work on maintaining coverage for pre-existing conditions," Barras said. "I greatly appreciate the Attorney General's respect of the separation of powers and his reverence of legislation being initiated by the House and Senate."

President Donald Trump's administration has refused to defend the Affordable Care Act against the lawsuit, though Democratic attorneys general from states such as California have stepped in to do so.

Still, the U.S. Department of Justice lawyer attending the courtroom proceedings last week argued against some of what Paxton, Landry and others are pushing to do with the lawsuit. He said U.S. District Judge Reed O'Connor should not issue an injunction to immediately halt Obamacare -- as Paxton, Landry and others desire -- because it would cause turmoil in the health care system.

"The department opposes any nationwide injunction," Justice Department Deputy Assistant Attorney General Brett Shumate said, according to The Dallas Morning News. "There could be a potential for chaos."